# significant Interaction between a significant discrete variable and non significant continuous variable

In my dataset, I have to test the effect of humidity on the height of plants. However, we have an extra effect which is nitrate on height. Each plant had a nitrate measurement but we had one group in "wet" category and another in "dry category" for humidity. We also divided our dataset into 6 populations and each population was either in the dry humidity or wet humidity. I want to test if there is an interaction between humidity and nitrate on the response variable height and I get a significant effect for humidity a non-significant effect for nitrate but a significant interaction between them. I used this model:

library(lme4)
library(lmerTest)
Ex$$population.f= factor(Ex$$population)
mixEx <- lmer(height~humidity+nitrate+ nitrate*humidity+(1|population.f:humidity),data=Ex)
anova(mixEx,ddf="Satterthwaite",type=3)
summary(mixEx)


Output:

> library(lme4)
> library(lmerTest)
> Ex$$population.f= factor(Ex$$population)
> mixEx<- lmer(height~humidity+nitrate+nitrate*humidity+ (1|population.f:humidity),data=Ex)
> anova(mixEx,ddf="Satterthwaite",type=3)
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF  DenDF  F value    Pr(>F)
humidity           2930    2930     1  4.654  61.5896  0.000745 ***
nitrate             107     107     1 82.000   2.2478  0.137643
humidity:nitrate  39426   39426     1 82.000 828.7753 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> summary(mixEx)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: height ~ humidity + nitrate + nitrate * humidity + (1 | population.f:humidity)
Data: Ex

REML criterion at convergence: 610.1

Scaled residuals:
Min       1Q   Median       3Q      Max
-2.32743 -0.55914 -0.01613  0.56248  2.91713

Random effects:
Groups                Name        Variance Std.Dev.
population.f:humidity (Intercept) 106.08   10.299
Residual                           47.57    6.897
Number of obs: 90, groups:  population.f:humidity, 6

Fixed effects:
Estimate Std. Error       df t value Pr(>|t|)
(Intercept)          74.9140     6.2680   4.6544  11.952 0.000114 ***
humiditywet         -69.5638     8.8640   4.6538  -7.848 0.000745 ***
nitrate              -6.4867     0.3364  82.0001 -19.284  < 2e-16 ***
humiditywet:nitrate  13.6861     0.4754  82.0002  28.788  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) hmdtyw nitrat
humiditywet -0.707
nitrate     -0.270  0.191
hmdtywt:ntr  0.191 -0.270 -0.708


I don't know how to interpret the results. If I remove the humidity: nitrate the humidity is not significant anymore for the height and the variance for the random effect of the population is a bit lower and that of the residual is significantly higher. This means this interaction explains variation in data. But I don't know what to conclude.

> library(lme4)
> library(lmerTest)
> Ex$$population.f= factor(Ex$$population)
> mixEx<- lmer(height~humidity+nitrate+ (1|population.f:humidity),data=Ex)
> anova(mixEx,ddf="Satterthwaite",type=3)
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF  DenDF F value Pr(>F)
humidity   2.613   2.613     1  4.000  0.0050 0.9470
nitrate  111.914 111.914     1 83.003  0.2144 0.6446
> summary(mixEx)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: height ~ humidity + nitrate + (1 | population.f:humidity)
Data: Ex

REML criterion at convergence: 810.2

Scaled residuals:
Min       1Q   Median       3Q      Max
-1.63438 -0.92226 -0.00655  0.87698  1.76434

Random effects:
Groups                Name        Variance Std.Dev.
population.f:humidity (Intercept)  72.79    8.532
Residual                          522.04   22.848
Number of obs: 90, groups:  population.f:humidity, 6

Fixed effects:
Estimate Std. Error      df t value Pr(>|t|)
(Intercept)  40.3973     7.1835  8.2043   5.624 0.000453 ***
humiditywet  -0.5992     8.4694  4.0000  -0.071 0.946997
nitrate       0.3646     0.7874 83.0026   0.463 0.644570
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
(Intr) hmdtyw
humiditywet -0.589
nitrate     -0.552  0.000

• Could you show the results? – The Laconic Dec 9 '18 at 17:04
• @TheLaconic yes i edited and added the answers – Tamara Bou Chahine Dec 9 '18 at 17:31